For the nominal-the-best problem, use the quadratic loss function L(y, t) =
c(y − t)
2 to measure the quality loss of deviation of the response y from the
target t. If there is an adjustment factor, use the two-step procedure to choose
optimal factor settings:
(i) Select levels of some factors to minimize Var(y).
(ii) Select the level of a factor not used in (i) to move E(y) closer to t.
An adjustment factor is a factor that has a significant effect on the mean but
not on the variance. See Section 4.10. To carry out this procedure in the data
analysis, use linear regression to model the sample average ȳ and the log sample variance ln s2 in terms of the factor effects. See the analysis in Section 4.12
for an illustration.
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